Multigrid methods for incompressible heat flow problems with an unknown interface

Finite-volume/multigrid methods are presented for solving incompressible heat flow problems with an unknown melt/solid interface, mainly in solidification applications, using primitive variables on collocated grids. The methods are implemented based on a multiblock and multilevel approach, allowing the treatment of a complicated geometry. The inner iterations are based on the SIMPLE scheme, in which the momentum interpolation is used to prevent velocity/pressure decoupling. The outer iterations are set up for interface update through the isotherm migration method. V-cycle and full multigrid (FMG) methods are tested for both two- and three-dimensional problems and are compared with a global Newton's method and a single-grid method. The effects of Prandtl and Rayleigh numbers on the performance of the schemes are also illustrated. Among these approaches, FMG has proven to be superior on performance and efficient for large problems. Sample calculations are also conducted for horizontal Bridgman crystal growth, and the performance is compared with that of traditional single-grid methods. (C) 1999 Academic Press.